3/4x+10=5-1/2x

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Solution for 3/4x+10=5-1/2x equation:



3/4x+10=5-1/2x
We move all terms to the left:
3/4x+10-(5-1/2x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
3/4x-(-1/2x+5)+10=0
We get rid of parentheses
3/4x+1/2x-5+10=0
We calculate fractions
6x/8x^2+4x/8x^2-5+10=0
We add all the numbers together, and all the variables
6x/8x^2+4x/8x^2+5=0
We multiply all the terms by the denominator
6x+4x+5*8x^2=0
We add all the numbers together, and all the variables
10x+5*8x^2=0
Wy multiply elements
40x^2+10x=0
a = 40; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·40·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*40}=\frac{-20}{80} =-1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*40}=\frac{0}{80} =0 $

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